The classic analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. In contrast, machine learning approaches shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take these predictions into account. In particular, we study the following online selection problems: (i) the classic secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classic online algorithm for each problem) when the predictions are sufficiently accurate. For each algorithm, we establish a trade-off between the competitive ratios obtained in the two respective cases.

在线算法的经典分析，由于其最坏情况的性质，当手头的输入实例远非最坏情况时，可能会非常悲观。相比之下，机器学习方法在利用过去输入中的模式来预测未来方面大放异彩。然而，这样的预测虽然通常是准确的，但也可能很差。受最近一系列工作的启发，我们用机器学习的关于未来的预测来增强三个著名的在线设置，并开发将这些预测考虑在内的算法。特别是，我们研究了以下在线选择问题：(i) 经典秘书问题，(ii) 在线二分匹配和 (iii) 图形拟阵秘书问题。我们的算法在预测低于标准的情况下仍然提供最坏情况下的性能保证，同时在预测足够准确时获得改进的竞争比（针对每个问题的最著名的经典在线算法）。对于每种算法，我们在两种情况下获得的竞争比率之间建立了权衡。